The two-Higgs-doublet model (2HDM), as one of the simplest extensions of the Standard Model (SM), is obtained by adding another scalar doublet to the SM and is featured by a pair of charged Higgs, which could affect many low-energy processes. In the "Higgs basis" for a generic 2HDM, only one scalar doublet gets a nonzero vacuum expectation value and, under the criterion of minimal flavor violation, the other one is fixed to be either color-singlet or color-octet, which are named as type III and type C 2HDM, respectively. In this paper, we study...